THE SPARK: Chalk up Friday's 12 percent gain to a quintessential relief rally. After the stock market closed Thursday, HP released quarterly earnings and revenue that topped the projections of the company's management and analysts.

Although the results showed that HP's PC business and other key operations are still slumping, the numbers were a soothing contrast to the company's ghastly performance during much of last year. In the previous two quarters alone, HP had registered losses totaling $15.3 billion, reflecting the costs of two major acquisitions that had gone awry. In the January quarter, it posted a $1.2 billion profit.

THE BIG PICTURE: Now that HP did better than expected in its fiscal first quarter, which ended in January, it's raised hopes that HP CEO Meg Whitman might be able to engineer a turnaround ahead of schedule. Whitman has consistently described her plan as a "multi-year journey."

HP, which is based in Palo, Alto, Calif., fed the optimism by predicting that its earnings for the current quarter will be slightly better than analysts' projections. Even so, Whitman cautioned in a Thursday conference call with analysts that HP still faces plenty of challenges. Among other things, the downturn in PC sales could still get even worse, according to HP. In the most recent quarter, revenue in HP's PC division fell 8 percent from the previous year.

Like most other PC makers, HP is scrambling to adapt to a technological shift that is driving more spending on smartphones and tablet computers instead of desktop and laptop machines.

Plenty of investors still have their doubts about HP's ability to evolve while it also tries to expand into more profitable technology niches such as business software, data-analysis tools and consulting services. Even after Friday's big boost, the shares are about 15 percent below where they stood when Whitman became CEO in September 2011. Over the past three years, shares have lost about 60 percent of their value.

ANALYST'S TAKE: Many analysts seem to think the market may have overreacted to HP's latest earnings report. One, Sterene Agee's Shaw Wu, said in a Friday research note that he didn't expect big future stock-market gains.

SHARE ACTION: HP's stock climbed $2.10, or 12 percent, to close at $19.20. That marked the company's biggest one-day gain since a 14.5 percent increase in November 2008 and left the shares at its highest closing price in six months.